I animated curve with hook modifiers. How can i export the animated curve?
Unfortunately this does not bode well for you. The problem seems three fold:


As far as I know there are currently no addons or exporters that can export Bezier Curves out of Blender. Most exchange formats I know support mesh data only anyway, they don't even have a concept of Bezier Curve, so to the best of my knowledge, non of the provided exporter addons can even write Bezier Curve data directly without explicit conversion to mesh first.
Exporting animations is hard, few file formats support animation data because it is hard to standardize, the exceptions I know here are Collada and FBX, and perhaps some other "cache based" formats like Alembic and similar.
Even those file formats that do support animations are frequently very limited in the type of data that can be exported. Mostly rigging and armature methods are supported, and even those often encounter issues and incompatibilities. Deformation based animations, morphing, shape keys, modifiers, and/or generated data like simulations, physics, fluids, etc, including hooks, are most likely not part of the small subset of animation techniques that can be exported.


So what options do you have? Not many.


Converting (a copy) of your animated bezier curve into a mesh and exporting that instead may alleviate some of the issues, but I can't see it going very far beyond conversion, you still need to export a deformation animation and that can be troublesome.
Exporting as an SVG file There is one third party addon SVG Export Script that exports the viewport as an SVG file. There is this one particular setting called Bezier Overlay that allows exporting Bezier Curve objects as SVG paths directly.
It is obviously limited to 2D curves (because SVG is an illustration image format) and it probably doesn't support deformation animations anyway. I believe it can export animations as a sequence of independent SVG files but nothing more.
Exporting hook animation only Depending on where you are exporting to (which you never state), what you intend to do with said animation, and the capabilities of the destination software, you may be able to get away with exporting only the hook positions, and rebuild your curve elsewhere from that info.